Transformation 3ph->SRF

Purpose

Transform 3-phase signal to stationary reference frame

Library

Control / Transformations

Description

This block transforms a three-phase signal \([x_\mathrm{a}\; x_\mathrm{b}\; x_\mathrm{c}]\) into a two-dimensional vector \([x_\alpha\; x_\beta]\) in the stationary reference frame:

\[\begin{split}\left[\!\! \begin{array}{c} x_\alpha \\[0.2cm] x_\beta \end{array} \! \! \right] = \frac{2}{3} \left[ \begin{array}{ccc} \displaystyle 1 & \displaystyle -\frac{1}{2} & \displaystyle -\frac{1}{2} \\[0.4cm] 0 & \displaystyle \frac{\sqrt{3}}{2} & \displaystyle -\frac{\sqrt{3}}{2} \end{array} \right] \cdot \left[\!\! \begin{array}{ccc} x_\mathrm{a} \\[0.2cm] x_\mathrm{b} \\[0.2cm] x_\mathrm{c} \end{array} \! \! \right]\end{split}\]

Any zero-sequence component in the three-phase signals is discarded.

Note

The stationary reference frame transfomation follows the axis alignment and rotation direction conventions presented in Conventions & Definitions.